Pavement material microwave moisture-density measurement methods and apparatuses

ABSTRACT

A portable microwave material gauge for determining the quality of a pavement material is provided. The gauge includes an electromagnetic field generator configured to generate an electric field mode that penetrates into the material wherein the material includes a heterogeneous material including at least one of a pavement material and a soil material, a calibration data set, a sensor of size and shape to support the electric field mode and to determine the response of the pavement material to the electric field wherein determining the response includes determining a change in the permittivity as a function of a change in the quality of the material; and an analyzer configured to correlate the sensor permittivity response to the calibration data set wherein correlating the response includes using stored relationships between the material quality and the sensor response using calibration samples having changes in permittivity as a function of quality.

RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication Ser. No. 60/514,031, filed Oct. 24, 2003; and is acontinuing application of U.S. patent application Ser. No. 13/846,181,filed on Mar. 18, 2013, which is a continuation application of U.S.patent application Ser. No. 11/712,060, filed on Feb. 28, 2007, which isa continuation of U.S. patent application Ser. No. 10/971,546, filedOct. 22, 2004; the disclosure of which is incorporated herein byreference in its entirety.

TECHNICAL FIELD

This invention relates to the measurement of the quality of a pavementmaterial such as soil, sand, aggregate, asphalt, and cement, and moreparticularly to a test instrument and method for measuring orcorrelating the density of a pavement sample using microwave bandwidths.The method is based on precise measurements of the real and imaginaryparts of the permittivity in the frequency or time domain. It also hasapplications for measuring the free water content of constructionmaterials.

BACKGROUND

Pavement materials, such as soil, sand, aggregate, asphalt, and cement,require quality testing for qualities such as moisture and density.Destructive tests and nondestructive tests are used throughout theindustry for determining these qualities. In laboratory destructivetests, cylindrical samples are prepared, typically with a gyratorycompactor, and various material properties are studied to determine thebest mix design for a pavement. In field destructive tests, cylindricalsamples are cored from test strips, newly constructed roads, or existingroads. The material properties of these samples are then used toevaluate whether the test strip or the new pavement meets the designcriteria and whether the existing road is in good operating condition orin need of repairs.

Currently, several methods are used for measuring the density ofcylindrical samples: dimensional analysis, the water displacementmethod, the paraffin coated method, and the para-film-covered method. Ineach case, the bulk density of a sample is derived by, as in thedefinition, dividing the dry sample mass by the estimated sample volume.All methods require a balance with a sensitivity of 0.1 g. to measurethe mass of the sample. In the dimensional analysis method, samplevolume is determined from the radius and thickness (height)measurements. Here, many readings of the radius and thickness of thesample are made using either manually vernier caliper or automaticallyusing a laser system. The average values of the radius and the thicknessare then used to calculate the sample volume.

Other methods use the Archimedes Principle for determining the samplevolume. These methods require a large container filled with clean water.The water temperature should be monitored and controlled at a specifictemperature, e.g. at 25° C. At one stage of the test, the sample is keptimmersed in water for approximately 4 minutes and the weight of thesample, while suspended in water, is recorded. In the “paraffin-coated”method, after determining the dry weight of the sample, a thin coatingof paraffin is applied to cover the entire surface area of the sample.Then, the sample is weighed again in air. Finally, the sample is weighedwhile immersed in water. More details can be found in standards ASTM D2726 for the water displacement method and ASTM D 1188 for theparaffin-coated method.

Nondestructive field measurements of asphalt are typically accomplishedwith nuclear gauges. Nuclear radiation gauges have been widely used formeasuring the density of soil and asphaltic materials. Such gaugestypically include a source of gamma radiation which directs gammaradiation into the test material, and a radiation detector locatedadjacent to the surface of the test material for detecting radiationscattered back to the surface. From this detector reading, adetermination of the density of the material can be made.

Nuclear gauges, however, require a high degree of training andradiological management for the operators of these gauges. Therefore, itwould be desirable to obtain accurate field measurement gauges withoutthe use of nuclear gauges.

SUMMARY

Methods and apparatuses for obtaining the density of a pavement materialsample by microwave electromagnetic analysis are therefore provided.According to one embodiment of the invention, a method of obtaining amaterial property of a pavement material from a microwave fieldgenerally includes generating a microwave frequency electromagneticfield of a first mode about the pavement material. The frequencyresponse of the pavement material in the electromagnetic field can bemeasured, such as by a network analyzer. One example of measuringfrequency response may include obtaining scattering parameters for thefrequency response although other frequency response parameters may beemployed. The measurement of the frequency response permits correlatingthe frequency response to a material property of the pavement materialsample, such as the density. Generally, the permittivity of a materialpermits direct correlation to the density of a material, andpermittivity is a convenient way to assess density. However, thefrequency response may be used to directly or indirectly calculate thedensity by other methods.

In further more particular embodiments of the invention, a method mayalso include calibration techniques. Calibration may be accomplished bygenerating a microwave frequency electromagnetic field of a first modeabout a calibration material. The calibration material should have knownphysical properties such as density, volume, specific gravity, orporosity. Similar to the measurement method, a frequency response of thecalibration material may be determined. The frequency response of thecalibration material may be correlated to the known physical propertiesof the calibration material, thus providing calibration curve for thefrequency response of the pavement material.

A method of correcting for the roughness of a pavement material is alsoprovided. Generally the roughness may permit dividing the pavement intoa shallow layer, the rough part, and a deep layer. Accordingly, a methodof determining the permittivity of a pavement material having a shallowlayer and a deep layer generally includes measuring a pavement materialwith first and second planar circuit permittivity sensors. The firstplanar circuit sensor measures the permittivity in a sample volumecorresponding to at least a portion of both the shallow layer and thedeep layer, the second planar circuit sensor measures permittivity in asample volume corresponding at least a portion of the shallow layer. Acalibration data set may be obtained for the first and second planarcircuit sensors by calibrating to a plurality of known pavement materialpermittivities. The first planar circuit sensor measures thepermittivity over the pavement material to permit determining a firstmeasured permittivity. The second planar circuit sensor over thepavement material to permit determining a second measured permittivity.The first permittivity and second permittivity are correlated with thecalibration data to determine the permittivity of the pavement material.

Additionally, embodiments of the invention include an apparatus forobtaining the density of a pavement sample. The apparatus generallyincludes a microwave circuit of a size and shape to generate anelectromagnetic field about a pavement material. A network analyzer isinterconnected to the microwave circuit to generate a microwave input tothe circuit for generating the electromagnetic field. The networkanalyzer should be capable of measuring at least one scatteringparameter. From the measured scattering parameter, the apparatus maydetermine the density of the pavement material.

An object of the presently disclosed subject matter having been statedhereinabove, and which is achieved in whole or in part by the presentlydisclosed subject matter, other objects will become evident as thedescription proceeds when taken in connection with the accompanyingdrawings as best described hereinbelow.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an apparatus for obtaining the density of a pavement materialaccording to one embodiment of the invention.

FIG. 2 is a diagram of an apparatus for obtaining the density of apavement material according to one embodiment of the invention.

FIG. 3 is a resonant cavity waveguide including a material sampleemployed for obtaining the density of a pavement material according toone embodiment of the invention.

FIG. 4 is a plot of finite element analysis and theoretical solution ofthe cavity and sample of FIG. 3 according to methods of one embodimentof the invention.

FIG. 5 is a ratio, K, of the finite element analysis for correction tothe theoretical solution as a function of dielectric constant accordingto methods of one embodiment of the invention.

FIG. 6 is a plot of frequency sweep of the cavity of FIG. 3 and a sampleillustrating the resonant frequency.

FIG. 7 is a plot of permittivities for a series of samples foundemploying methods according to one embodiment of the invention for aseries of samples having known densities.

FIG. 8 is a plot of densities for a series of samples found according tomethods of one embodiment of the invention compared to densities foundby independent methods.

FIG. 9 is an electrical equivalent diagram of a tuned resonant cavity.

FIG. 10 is an electrical equivalent diagram of a detuned short microwavecavity according to one embodiment of the present invention.

FIG. 11 is a plot of voltage standing wave ratio of a cavity accordingto one embodiment of the present invention.

FIG. 12 is a smith chart plot of impedance of a cavity according to oneembodiment of the present invention.

FIG. 13 is a plot of frequency sweep of a cavity and a sampleillustrating the resonant frequency found according to methods of oneembodiment of the invention.

FIG. 14 is a plot of densities and resonant frequencies from differentsamples according to methods of one embodiment of the invention.

FIG. 15 is a plot of slotline impedance and density for a planarmicrowave circuit according to one embodiment of the present invention.

FIGS. 16(a) and (b) are microstrip microwave elements for obtaining thedensity of a pave material according to one embodiment of the invention.

FIG. 17 is a microstrip microwave element for obtaining the density of apavement material according to one embodiment of the invention.

FIG. 18 is a plot of resonant frequency response to changes in densityof samples tested by a microstrip microwave element for obtaining thedensity of a pavement material according to methods of one embodiment ofthe invention.

FIGS. 19(a) and (b) are plots of frequency and quality factor responsesfor samples of different densities tested by a microstrip microwaveelement for obtaining the density of a pave material according tomethods of one embodiment of the invention.

FIG. 20 is a microstrip microwave element disposed over a pavementmaterial for obtaining the density of the pavement material according tomethods of one embodiment of the invention.

FIG. 21 is a plot of permittivity measurement of a deep layer of apavement material to obtain a surface roughness correction according toembodiments and methods of the present invention.

FIG. 22 is a plot of ratios of shallow and deep measurements of apavement material to obtain a surface roughness correction according toembodiments and methods of the present invention.

FIG. 23 is a plot of ratios of shallow measurements and deep measurementof a pavement material sample to obtain a surface roughness correctionaccording to embodiments and methods of the present invention.

DETAILED DESCRIPTION

The present inventions now will be described more fully hereinafter withreference to the accompanying drawings, in which some, but not allembodiments of the inventions are shown. Indeed, these inventions may beembodied in many different forms and should not be construed as limitedto the embodiments set forth herein; rather, these embodiments areprovided so that this disclosure will satisfy applicable legalrequirements. Like numbers refer to like elements throughout.

Pavement materials, asphalt in particular, are heterogeneous mixtures ofair, rocks, and binder. Each of these materials has a particularpermittivity (i.e. the dielectric constant) associated with its abilityto be polarized by an electric field. The permittivity is linearlyrelated to the polarizability and is a complex quantity. Thepermittivity is generally complex having real,

′, and imaginary components,

″, representing energy storage and energy loss respectively to apropagating electromagnetic wave. Typically, when speaking of thedielectric constant one is referring to the real part of thepermittivity.

Air has a dielectric constant of 1.0, asphalt binders have dielectricconstant between 2.0 and 4.0, and rocks have dielectric constants thatvary, but granite is about 4.0. In a moisture measuring mode, themicrowave device would be used to measure the volume or mass percent offree water. Free water has a dielectric constant of 80 or less dependingon the temperature. Bound water has a dielectric constant near that ofice of about 3 or 4. For a complicated heterogeneous mixture ofmaterials like soil and water, the permittivity can be a strong functionof frequency when measured swept over a 1 Ghz bandwidth. For HMA (hotmix asphalt), the aggregate is dried, and any residing water is bound tothe aggregate. Bound moisture has a dielectric constant near 3 or 4.This is close to the permittivity of the binder and dry aggregates, andis not problematic as long as the mix remains consistent.

The measured permittivity of a material depends on the frequency and thetype of charge carrier that is being displaced by an applied electricfield. These charge carriers are displaced thus forming a net dipolemoment. The charges can be electronic, atomic, polar and ionic. Inasphalt, all of the above mechanisms contribute to the apparentdielectric constant. However, the main contributions are due to thepolar and ionic responses, on a per unit volume basis. Additionalsolvents or impurities such as water will increase these contributionsand the apparent dielectric constant. For low frequencies, the heavyions respond and the Maxwell-Wagner effect makes the asphalt appearstrongly polar and temperature dependent. At microwave frequencies, thiseffect is nonexistent. The Maxwell-Wagner effect also allows for thequantification of soil moisture and density of the heterogeneousmaterials.

The behavior of polar molecules in the asphalt follows afrequency-temperature response that can be modeled with a modified Debyeequation. The dispersion in the microwave region is significantlydecreased as a result of the reduction of the relaxation frequency. Thisreduction is anticipated due to the heavy asphalt molecules, and becauseof the asphalt bonding to the aggregate, which is of course the purposeof adding the binder in the first place.

Although the asphalt liquid is characterized as non-magnetic, theaggregates that make up the pavement mix could very well have a magneticmoment leading to a complex permeability μ′-j μ″. Here, μ′ is the realpart representing the ability to store magnetic energy, and μ″ is theimaginary part representing loss. Since both

and μ can slow an electromagnetic wave, and both increase on a per unitvolume basis with compaction, the permeability could play a role in themeasurement of the asphalt density, but only if a substantial magneticfield H exists in the material. Likewise,

″ and μ″ will increase the energy loss with compaction. It has beensuggested to add lossy ferrite oxides to an asphalt mix in order toincrease the efficiency of microwave heating. The asphalt can be heatedduring application to maintain temperature, or during repairs orremoval.

Referring to FIG. 1, one method of measuring real and imaginary parts ofpermittivity is defined by ASTM Standard D2520-95, which is herebyincorporated by reference. The test method of D2520 is based onmicrowave measurement of the complex scattering (S) parametersthroughout a specimen in a resonant transmission line or closed cavity.In this technique, the sample is placed inside a transmission line orcavity and is the device under test (DUT) 10. The methods hereinincorporate these teachings and further can be extended to leaky typeresonators. The measurements may be implemented by a network analyzer 20analyzing the wave propagation through the material specimen usingS-parameter analysis. They can be implemented also by analyzing the wavepropagation through a transmission line or waveguide and interactingwith the material at the boundary of the sensor.

S-parameter analysis techniques may be accomplished by a variety ofcommercially available broadband network analyzers, such as the HP(Agilent) 8753 Network Analyzer manufactured by Agilent Technologies,Inc. of Palo Alto, Calif., as shown in FIG. 1. Network analyzers 20 arewell known to those of ordinary skill in the art for measuring thevoltage standing wave ratio, complex reflection/transmissioncoefficients, impedance and admittance matrix parameters, and return andinsertion loss of a device under test. The setup typically includes thenetwork analyzer 20, a transmission/reflection test set 22, and thedevice under test 10, which is described in various embodiments below.These instruments are capable of both frequency and time domainanalysis. The conversion between these two domains is accomplished usingthe Fast Fourier Transform commonly known as the FFT. For example, animpulse or step response can be analyzed for dispersion and groupvelocity. The velocity is inversely related to the real part of thedielectric constant and in fact proportional to 1/√

′(ω) whereas the loss is related to the imaginary part

″(ω). Hence, both the real and imaginary parts can be frequencydependent, as one skilled in the art would know. These days it is nowpossible to economically build and design one port and full two portnetwork analyzers that are compact and efficient on battery power.

FIG. 2 is a simplified diagram of a network analyzer 20, including afrequency generator 8, illustrating the switching network 12, 14 anddirectional couplers 16, 18 for a full two port system to a DUT 10.There are many designs that could be used for the network analysisincluding scaler and vector network analyzers, some use simple diodedetectors as can be found in publications like “Microwave ImpedanceMeasurement by P. I. Somlo, B S J. D. Hunter, Peter Peregrinus Lt.,London UK. 1985, or Microwave Measurement Edited by A. e. Bailey, PeterPeregrinus Lt., London UK. 1985. Reflectometers, VSWR bridges, andnetwork analyzers can be based on bridge circuitry for lowerfrequencies, and couplers for the higher frequencies.

Impedance, permittivity, permeability, complex permittivity, and complexpermeability of a material can be measured using S-parameter analysis,such as described in Agilent AN 154 S-parameter Design Application Note,which is hereby incorporated by reference. As S-parameters relate ratiosof RF network inputs to outputs, they can be used to measure the ratiosof RF network inputs and outputs for a material placed within a closedchamber or near an open sensor system. An incident RF electromagneticwave is actively excited and the system responds according to theboundary conditions and constitutive relations of the material. Forexample, S₁₁ is a reflection measurement from the device under test thatmay yield return loss. S₁₂ is a transmission measurement through thedevice under test that may yield insertion loss. As such, S₁₁ and S₁₂may be measured as a ratio of the RF input and output, in magnitude andphase. Hence these embodiments of the invention employ a measuringsystem comprising a wideband microwave sensor for exciting the DUT, acoupler, and a measuring circuit allowing scattering (S) parameters,impedance (Z) matrix parameters, or admittance matrix (Y) parameters anda data processing unit with display and software. From these,calculations of stored energy in a near field, parameters such aspropagation constants α, β, resonant frequency and Q, and phase andgroup velocity can be deduced. From these (not limited to thesespecifically) a resulting property of the sample is found. The systemuses a microwave sweeping oscillator to permit measuring the parameterssuch as the scattering parameters and other matrix parameters as afunction of frequency, such as to locate a resonant frequency, Q,maximum or minimum of S₁₁ or S₂₁ as a function of frequency. The displayand software could be integrated into a single unit much like a Troxler3440 Nuclear gauge. This instrument incorporates downhole as well assurface measurements. The processing unit and display could be linked toa PDA using a wire or wireless connection. The software would includeall the basic commands in addition to project management programs.

While material measurements have been described in conjunction withnetwork analyzers to determine parameters such as impedance,permittivity, permeability, complex permittivity, and complexpermeability by using S-parameters, it will be understood by those ofordinary skill in the art that other measurement systems utilizing othermaterial analysis techniques may be used in conjunction with thesemethods and the device under test described herein. In fact, anyelectromagnetic wave analysis procedures that permit determinations ofpermittivity and complex permittivity either via software or manualmethods, may be implemented in conjunction with the present inventionwithout departing form the spirit or scope of the claims.

Resonant Cavity Sample Gauge

In the asphalt pavement construction industry, the cylindrical asphaltcore is a common sample geometry. Accordingly, asphalt cylinders mayadvantageously be used in a resonant cavity to determine permittivityproperties. According to one embodiment of a method of determining thedensity of an asphalt sample, the permittivity analysis may yielddensity measurements. These results could be used to calibrate fieldinstruments. It should be noted that while a rectangular resonant cavityis described below as an appropriate measurement device for an asphaltsample, other resonant devices are known to those of ordinary skill inthe art and may be substituted accordingly. Other waveguide resonatorsinclude cylindrical, reentrant, Fabry Perot, or the devices made frommicrostrip, slotline, coplanar waveguide, coplanar strips, surfacewaveguide, dielectric resonator and any of a number of resonatingstructures and modes such as TEM, quasi-TEM, TE, TM, or hybrid HE modes.The measurements could be made in the reflection mode, transmission modeor combinations thereof. The structures could have loads to satisfycertain boundary conditions such as open, short, match, or even aresonant load such as a short or resonant dipole. Here, the dipole wouldreact with the near field and the impedance would shift the resonantfrequency of the feed. These could be realized using a microstrip patchantenna, or even an antenna array, such as described in “A New Method ofMeasuring Dielectric Constant Using the Resonant Frequency of a PatchAntenna”, Du Shimin, IEEE Transactions of Microwave Theory andTechniques, No. 9, September 1996. In any event, the microwave radiationwill interact in the near field with the material under test for contactdevices, and in the far field for non-contact devices or deepermeasurements.

As described herein, it should also be noted that the sample is notnecessarily small compared to a wavelength, but asphalt samples have adielectric constant typically less than about 8 and are constant inshape. As such, a constant shape of both calibration samples andmeasured samples permits shape error to be corrected. The large size ofthe sample, as compared to the wavelength, can be corrected for with acorrection factor K. The correction factor may be found using a finiteelement analysis or any number of numerical computational techniques,discussed in more detail below. If it is a common shape such as a smallcube or rod it is possible to obtain corrections using rigorousmathematics with appropriate boundary conditions, but in general, theFinite Element or other numerical techniques are useful for anygeometry. Other numerical techniques include finite difference, finitedifference time domain, method of moments, etc. Therefore, the abilityto disregard shape, the ability to correct for size, and the relativelylow dielectric constant permits perturbation techniques or in general“wave like propagation” methods to be used to measure the permittivityof asphalt samples or surfaces. The sensors can be used for spotchecking an asphalt or soil surface, or a surface wave could be launchedand detected covering larger areas. It is well known that a surface wavehas a penetration depth inversely proportional to the frequency ofexcitation. This device could be a slow wave structure such as acorrugated slab in contact with the medium of interest. The propagationconstant as a function of frequency could then yield information of thequality vs. depth.

The following illustrates one method according to one embodiment of theinvention for obtaining the density of an asphalt sample from apermittivity analysis. Referring now to FIG. 3, a rectangular TE₁₀₁ moderesonant cavity 32, which is may be one embodiment of the DUT in FIG. 1,was used to obtain measurements of an asphalt sample 34. Thisrectangular resonant cavity has dimensions of 0.9×0.4×0.19 meters. ASTMstandard D-2520 is a standard for small samples that meet certainboundary conditions that may be employed with boundary valuemodifications. In the standard, the sample is presumed to be thin andextends all the way through the cavity. Such a sample allows for easysolutions of Maxwell's Equations and the necessary energy analysis.First, the small sample does not “perturb the fields” hence you canassume that the field configuration is exactly the same before and afterinsertion. Furthermore you can calculate the fields of the empty cavity,and use the same solutions for the loaded cavity. Also, with this setupand mode, the sample is always tangent to the fields and there are noperpendicular fields interacting with the sample. This assures that thefield in the sample is exactly the same as with the empty cavity.

In FIG. 3, however, there is a large sample 32 that sits in the bottomof the cavity 34. From boundary conditions the field inside the samplewill be different from the empty cavity, as we have normal components.Also since the sample 32 is about 0.15 m wide and 0.1 m tall it is nolonger electrically small compared to a wavelength. So the ASTM boundaryconditions do not apply if the sample does not extend fully from top tobottom, or was not always tangent to the electric field. It would beconvenient to have air gaps between the cavity 34 and the sample 32 sothat it inserted easily, and this would require some correction as well.

For an empty, air filled, rectangular cavity the resonant frequency isfound by solving Maxwell's Equations with the appropriate boundaryconditions, so every resonant structure will have its own uniquerelationship for resonant frequency.

The fundamental mode for the rectangular cavity is

$\begin{matrix}{f_{101} = {\frac{c}{2\pi\sqrt{\mu_{0}ɛ_{0}}}\sqrt{\left( \frac{\pi}{width} \right)^{2} + \left( \frac{\pi}{length} \right)^{2}}}} & (1)\end{matrix}$

For this example cavity 32, the empty resonant frequency isapproximately 428 MHz. It is known from perturbation theory that

$\begin{matrix}\begin{matrix}{\frac{\delta\; f}{f} = {\frac{f_{2} - f_{1}}{f_{2}} + {\frac{j}{2}\left( {\frac{1}{Q_{2}} - \frac{1}{Q_{1}}} \right)}}} \\{= {{- \frac{\left( {ɛ_{r} - 1} \right)}{2}}\frac{\int_{V_{sample}}{{{E_{1} \cdot E_{2}}}^{2}{dv}}}{\int_{V_{Cavity}}{{E_{1}}^{2}{dv}}}}}\end{matrix} & (2)\end{matrix}$

(See R. F. Harrington, “Time Harmonic Electromagnetic Fields”, McGrawHill Book Co., 1961.) Where E₁, f₁ and Q₁ are the electric field,frequency and quality factor for the empty cavity and E₂, f₂ and Q₂ arefor the cavity containing the sample 34, while V_(cavity) and V_(sample)are the volumes of the cavity 32 and sample respectively. The qualityfactor Q is the ratio of energy stored in the system to that which isdissipated per cycle. For a transmission type resonator, it is measuredusing the 3 db bandwidth and the resonant frequency of theconfiguration. The quality factor is defined for any resonant systemwhether it is a waveguide cavity, a microstrip resonator, a resonanttransmission line or a cavity backed antenna.

For an unperturbed TE₁₀₁ mode cavity the electric field intensity, E, is

$\begin{matrix}{E_{y} = {E_{0}\sin\frac{\pi\; x}{a}\sin\frac{\pi\; z}{d}}} & (3)\end{matrix}$where a is the width of the cavity and d the length in meters.

Assuming for small samples that E₁=E₂, Equation 3 may be substitutedinto Equation 2 resulting in the solution for real and imaginary partsof permittivity, as:

$\begin{matrix}{{\frac{f_{2} - f_{1}}{f_{2}} + {\frac{j}{2}\left( {\frac{1}{Q_{2}} - \frac{1}{Q_{1}}} \right)}} = {{- \frac{ɛ^{\prime} - 1 - ɛ^{''}}{2}}\left( \frac{4V_{sample}}{V_{cavity}} \right)}} & (4)\end{matrix}$

Such that

$\begin{matrix}{ɛ^{\prime} = {{\frac{f_{1} - f_{2}}{2f_{2}K}\frac{V_{cavity}}{V_{sample}}} + 1}} & (5) \\{ɛ^{\prime} = {{\frac{1}{4}\frac{V_{cavity}}{V_{sample}K^{2}}\left( {\frac{1}{Q_{2}} - \frac{1}{Q_{1}}} \right)} = {\sigma\; l\;{\omega ɛ}_{0}}}} & (6)\end{matrix}$where σ represents the conductivity of the asphalt sample and K is thegeometrical correction factor and accounts for the change in theelectromagnetic fields with shape, permittivity and orientation. For asmall sample whereby the tangential E field is continuous across theboundary and throughout the sample K=1. However, for larger samples orsamples not oriented parallel with the fields, K must be determined byclosed form or using a numerical method such as finite element analysis.In general, the electric field E₂ is only found in context with theknowledge of the sample geometry, material properties and fieldorientation. The sensitivity is maximized when the E field is parallelto the sample boundary, but the analysis works for normal fields orcombinations thereof.

The finite element analysis requires modeling a “virtual” sample havingknown dielectric properties and dimensions. The analysis thereforeyields the complex frequency response of the system. For example, thecomplex propagation constant, resonant frequency and loss effects can beobtained. The finite element results may then be compared to actualmeasurements, and the parameters in the finite element model adjusteduntil the model produces exactly the same results as the measurementsover a bandwidth. Hence, a solution to the material parameters isindirectly found. This is computationally extensive, and could requirehours to find a solution.

In another approach, curves of resonant frequency or loss vs.permittivity and sample dimension could be found using the computationaltechniques and stored in a computer. Then in the portable device, thesample dimensions could be entered into the computer along with the lossand frequency results, and the complex permittivity could be found.Still, if the sample geometries are of standard shape as in the asphaltindustry, correction factors to closed form equations can be obtained asis the case of Equations 5 and 6. The correction factors could also beobtained experimentally if one possesses standard materials of knownpermittivity and constant geometry from sample to sample to use forcalibration. It was found that the correction factor for larger samplescould be used for smaller samples of the same general shape.

Typically, when a sample dimension is less than about λ/10 it can beconsidered electrically small. In these experiments, the pucks areusually about 150 mm in diameter, and 115 mm high. In the rectangularwave-guide used in these experiments, the first mode resonated at about426 MHz in air with a wavelength of about 750 mm. So the sample is notconsidered small, and furthermore, it does not extend to the top of thewave-guide. This gap between the sample and the wave-guide roof is anormal E field boundary condition, which will substantially change thefields in this region for

_(r)>1. This will further remove the solution from the ideal case.

The difference between the ideal solution and the FEM solution with theshort sample puck of material is illustrated in FIG. 4. A finite elementsimulation was carried out using a rectangular cavity of the dimensions0.9144×0.1905×0.3794 m. Inside the cavity and placed at the point ofmaximum electric field (the center for the fundamental mode) was avirtual cylindrical puck with a radius of 75.057 mm and a height of 115mm. In the numerical analysis, the permittivity was changed from 1 to 8.For an air filled cavity, it was found that the numerical analysis gavea resonant frequency f₁=427.6 MHz. With some adjustment of the magneticloop coupling mechanism this agreed exactly with the actual measuredvalue. The program was then run with the different permittivities, andeach time the Eigen-frequencies were recorded. The frequencies are shownin columns 4 and 5 of Table 1 below.

TABLE 1 δf/f₁ (theory d << λ, δf/f₁ (Finite f₁ (Finite f₁ (theory)

_(r)′ K = 1) elements) Element) K = 1 1.0 0 0 427.6 Mhz 427.6 Mhz 1.1.00616 .00538 425.31 424.98 1.2 .0123 .0107 423.08 422.40 1.3 .0185.0159 420.89 419.83 1.4 .0246 .0211 418.75 417.33 1.5 .0308 .0263 416.65414.82 2 .06158 .0508 406.94 402.8 3 .1232 .0944 390.70 380.70 4 .1848.1315 377.92 360.90 5 .2463 .1628 637.72 343.10 6 .3079 .1896 359.44326.94 7 .3695 .2127 352.60 312.23 8 .4311 .2327 346.89 298.79

In Table 1 δf=f₁−f₂ and the “theory” columns refer to the use ofEquations 5 and 6 with K=1. The correction factor K can be found foreach sample by simply dividing column 3 by column 2. FIG. 5 is a plot ofK vs.

_(r) for this geometry. In equation form, the correction factor wasfound to beK=0.0477+0.9*exp(−0.076

_(r))  (6b)

As an example using the real part of the permittivity, a calibrationsample was inserted into the cavity. In one example, the calibrationsample was a polyethylene puck of radius 74.95 m, height of 114.5 mm andpermittivity of 2.6 The frequency was swept over the proper band for thefirst resonance and is shown in FIG. 6. Here we see that the resonantfrequency is 400.08 MHz. Substituting this into Equation 5 with K=1yields a dielectric constant of

_(r)=1+(66.09/2.021)(427.6−400.08)/(2*400.08)or

_(r)=2.09. Multiplying this by K found from (6b) results in a value of2.57. Notice that the height of the polyethylene cylinder was notexactly the same as that which was used in the FE simulation. As long asthe measurement geometry is relatively close to the simulation, goodresults can be obtained. For larger differences in height h, acorrection for the permittivity can be estimated using

_(r)=(

_(r)−1)h/115+1  (6c)

This is derived using the fact that the frequency shift is proportionalto the ratio of volumes of the sample and the cavity Vs/Vc.

As a test incorporating the imaginary part of the permittivity it isknown that DELRIN, a well-known plastic, has a complex permittivity of3.1+j0.148. First a small sample was simulated using the finite elementprogram. This sample extended from the floor to the ceiling of thecavity and was only 25.4 mm in diameter. This gave a sample volume of96.528e−3 m³. Since the electric field vectors are always parallel tothe sample, and the sample is small compared to a wavelength, K=1.Equation (5) and (6) gives a resonant frequency of 424.99 Mhz and a Q of1104. As a check of the numerical program, this material was coded upand it was found that the Finite element analysis yields f=424.94 Mhzand a Q of 1056. A near perfect agreement. Next in the model, the Delrinwas expanded in size to have a radius of 75.057 mm and shortened to aheight of 115.0 mm leaving a substantial air gap between the sample andthe cavity ceiling. According to Table 1, this would result in a K of0.7666. Incorporating K into (5) and (6), and backsolving for frequencywe find f₂=389.21 Mhz. Likewise, Equation (6) results in a quality of93.1, both agreeing well with the numerical analysis. Therefore, it wasconcluded that even with large samples, the geometrical correctionfactor derived only from the real part of the permittivity could also beused for the imaginary calculations, and in fact, could be absorbed intothe shape factor.

To summarize, for the above described cavity, FIG. 4 illustrates theTE₁₀₁ response for a finite element analysis in comparison to thetypical ASTM 2520 method where the field E is not perturbed by theinsertion of the sample. FIG. 5, illustrates the correction factor K asa function of dielectric constant. Furthermore, during the course of theanalysis it was observed that the correction factors for both loss andfrequency shift (thus real and imaginary permittivity) were very close.Therefore it deemed acceptable to assume the same correction factor forboth the real part and the imaginary part of the permittivity. As such,the absolute permittivity of the sample may be determined from the aboveequations; even for electrically large and odd shaped samples.

For circuits, the quality measurements require correction for impedanceloading and loss other than from the sample properties and measurements.For an unloaded device,

$\begin{matrix}{\frac{1}{Q_{L\; 1}} = {\frac{1}{Q_{0}} + \frac{1}{Q_{E}}}} & (7)\end{matrix}$where Q_(L1) represents the total sum of all losses, Q_(O) is theinternal energy loss, and QE is the external energy loss through thecoaxial cable and network analyzer. For a device loaded with a sample,

$\begin{matrix}{\frac{1}{Q_{L\; 2}} = {\frac{1}{Q_{0}} + \frac{1}{Q_{E}} + \frac{1}{Q_{s}}}} & (8)\end{matrix}$

Accordingly, the sample Q may be determined by

$\begin{matrix}{{\frac{1}{Q_{L\; 1}} - \frac{1}{Q_{L\; 2}}} = \frac{1}{Q_{s}}} & (9)\end{matrix}$

For all three loss mechanisms, the loss equation is

$\begin{matrix}{Q_{L} = \frac{\omega\; L}{R_{s} + R_{sample} + Z_{0}}} & (10)\end{matrix}$where R_(s) represents internal losses for example the surfaceresistance of the resonator, R_(sample) represents the loss of thesample, and Z_(O) represents the impedance of the coaxial cable orpossibly other external losses such as radiation. At resonance, acoupling factor, β, relates Q_(O) and Q_(L) [R. E. Collin “Foundationsfor Microwave Engineering”, McGraw Hill, 1966.]Q _(O) =Q _(L)(1+β)  (11)wherein β is either overcoupled,β=R′/Z _(O)  (12)undercoupled,β=Z _(O) /R′  (13)or critically coupled.β=1  (14)

It is therefore advantageous to undercouple such that β<<1, toapproximateQ _(L) =Q _(S)  (16)

To summarize, the purpose of the cavity measurements of a calibrationsample is to obtain the complex permittivity of mix materials forcalibration of field devices, and to obtain these properties forlaboratory records of the engineering properties of cores. Theengineering properties are related to the quality of the cores throughthe chemistry of the binder (oxidation), water and void content of thecores.

Now when the permittivity of the asphalt sample has been established,the cavity can be calibrated with multiple asphalt samples of a knowndensity. For example, at least two samples of different density but ofthe same mix (permittivity characteristics) are placed in the resonatorto obtain measurements of Δf or ΔQ resulting in a linear equation fordensity. However, since most mixes have similar slopes, a genericcalibration curve could be obtained by finding only an offset of thecalibration curve. Here, only one asphalt sample of particularpermittivity and known density would be needed.

The simple model incorporated the dimensions of the puck, and a variablepermittivity. The different mixes have different “base” permittivitiesthat are reduced by the increase in air voids, as the density decreases.

Density Relations

As the material is compacted, the dipole density increases and thus both

′ and

″ will increase. These increases will decrease the phase velocity of theelectromagnetic wave, and increase the insertion and return loss of thesystem. For a resonant structure, both the resonant frequency and the Qwill decrease with increasing compaction. Off resonance, the magnitudeand phase of the reflection and transmission coefficients will change inaccordance with the characteristics and length of the waveguidingstructure, in this example a resonant cavity. As a result, it ispossible to measure density increases using

′ and/or

″ increases, or decreases in f and/or Q. With these types ofmeasurements, a calibration using calibration samples of known densitiesand consistent shape is necessary. If the calibration is performed usingSUPERPAVE type asphalt cores of radius about 75 mm and heights near 115mm vs. f and Q, then the calibration curves will be restricted to theseshapes and sizes; except for some height variation that could becorrected using (6c). In other words, the smaller Marshall pills couldnot be used without a separate calibration, as their radius is about 50mm. On the other hand, if the density calibrations are defined using thecomplex permittivity, then no matter what the shape of the sample, thecalibration will hold once the permittivity of the sample is measured.

Shape independent calibrations can be incorporated by taking the ratioof Equations (5) and the square root of (6) such as described in U.S.Pat. No. 5,554,935. Incorporating the fact that V_(s)=mass/ρ where ρ isthe bulk density we findρ=(G/(

f√Q)+C ²  (6d)where C is a constant. With this approach, frequency and Q can be usedwith the same calibration equation for different shapes.

Frequency Only Calibration

37 cores were produced in a Gyratory compactor. These were of thespecies of limestone and granite. There were 6 series of cores. Witheach series, three different void ratios were targeted in the mix byvarying the mass of the materials for a particular compaction height.The height was near 115 mm just like the simulations, and there were twoduplicates for each density.

In the cavity, two measurements were obtained for each corecharacterized by flipping the sample upside down. So each series had 6measurements. In the cavity, the sample is inserted and the frequencyshifts down from the empty 426.7 MHz value. Analysis at multiplefrequencies is desirable and could be obtained by selecting higher ordermodes or designing a different cavity.

From the finite element analysis, an equation was derived that directlyrelates the resonant frequency to the permittivity and

′=−0.7690+7355.34 exp(−0.0194f)where f is in MHz. Since the frequency shift is directly related to theratio of volumes Vs/Vc, then for different sample heights a correctionfor the permittivity can be estimated using Equation (6c). Theserelationships were used to find the real part of the dielectricconstants of the cores made in the laboratory. The results were thenused to obtain equations relating the permittivity to the density. Thedensities of the cores were obtained using nuclear instruments andmeasuring methods.

As an example, consider the series 2-xxx cores. For the core 2-102, thefrequency easily converts to a dielectric constant. The measurementresults are shown in Table 2 below where height correction wasincorporated using 6c. The X and O represent measurements whereby thecore was physically flipped in the cavity.

TABLE 2 Freq S21 DeltaF QL X 368.5625 −19.4509 0.72594 507.701 O368.3375 −19.8601 0.76284 482.8496 AVG PCF PCF (X) SampleID Height mm(gmb) (nuclear) mass (g) Microwave 2-102 113.900 2.032 126.472 4102.9126.291 Freq S21 DeltaF QL 368.5625 −19.4509 0.72594 507.701 epsX eppsXfact epsO eppsO fact 5.00 0.039064 0.639827 5.028544 0.041223 0.638667

For each different mix, a regression analysis was performed to obtainthe calibration curve for that mix vs. the permittivity. Table 3 showsthe results for series 2.

TABLE 3 CORE er′ er″ PCF slope intercept 2-102 5.042 0.039 126.47217.444 38.340 Flip core 5.067 0.041 126.472 0.376 2.088841 2-103 5.0580.035 126.196 0.994 0.570606 5.067 0.039 126.196 2264.960 14.000 2-2015.726 0.042 138.511 737.450 4.558272 5.740 0.047 138.511 2-202 5.7250.040 138.911 5.728 0.042 138.911 2-203 5.722 0.043 138.929 5.739 0040138.929 2-301 6.060 0.038 144.228 6.043 0.036 144.228 2-303 6.042 0.040143.019 6.062 0.042 143.019 2-305 6.074 0.042 143.890 6.074 0.038143.890

The residual is 0.994. A very good value representing a linearrelationship between the microwave dielectric constant and the densityof the cores.

Note that δf or δQ can be used as a function of density, or

′ and/or

″ as a function of density. Alternatively, ratios of these parametersmay be used such as

′/

″. An example is illustrated in FIG. 7 depicting

′ vs. ρ from the scattering coefficient (S₁₂) results of severaldifferent asphalt mixes. Note that FIG. 7 illustrates only the real partof permittivity. Also, each mix has different intercepts but similarslopes. Accordingly, it is acceptable to assume for these asphalt mixesthat all of the curves may be approximated to a single slope and thenonly the intercept needs to be found. This approximation may assist toreduce field calibration steps, however, the preferred method is tooffset both the slope and intercept. FIG. 8 illustrates the accuracywhen each mix is calibrated for both slope and intercept.

For a single mix design, both S₁₁ and S₁₂ can be used to correlatebetween frequency shift and density, thus disregarding actualpermittivity values in this case. In the field, measurements of the fand Q values or S₁₁ and S₁₂ can be easily correlated to the density of atest strip using cores or nuclear gauges without direct knowledge fromthe permittivity.

Reflection S₁₁

When a transmission line is terminated with a complex impedance,reflection measurements are appropriate. As is well known in themicrowave analysis, the impedance is measured at a port, and the phaseof this port (partly determined be the length from the device or load)defines the impedance in a predictable and cyclic manner. In particular,two common equivalent circuits can be obtained and are defined by the“detuned” resonance One is the detuned short position, and the other isthe detuned open position. Of course the equivalent circuit can take onan infinite number of impedances in between these extremes, but withproper referencing, the characteristics of the device can be extracted.Since the detuned short and open are mathematically dual to one another,the results of one can easily be carried to the other.

A tuned circuit is represented by FIG. 9 where a transmission lineimpedance Z_(O), a coupling resistance Rs and the cavity loss G, andelectric effect is C, and magnetic field effect is inductance L. Theresonator as a detuned short circuit is shown in the FIG. 10, and thereal and imaginary parts are proportional to the square of the couplingturns ratio n. Note that far off resonance, the circuit has theimpedance of a short in the ideal case. This feature could be used tocalibrate the systematic error of the network analyzer. For a microwavedevice, other resonances also effect the results. These models representthe response only near a particular harmonic. The impedance of the TE011detuned cavity is shown in the following figure in a Smith Chart format,FIG. 10. Here the reference plane has been shifted to represent a shortoff resonance.

It should be noted that impedance plot 40 of FIG. 12 is nearly circular.Near the resonance, the resistance or loss is constant with frequency,and this loss is modeled as a constant resistance circle on the SmithChart. At resonance, the impedance is real, and is closest to the centerof the chart leading to a minimum VSWR. For a well matched device, thereflection coefficient in dB will have a very sharp dip making it easyto find the resonance frequency.

A plot of VSWR near resonance is shown in FIG. 11. The procedure is tosweep the network analyzer over the pass band of the device and plot theVSWR as shown in FIG. 11.

For reflection measurements, the resonance corresponds to a minimumreflection coefficient or VSWR. As known in the art, it is also possibleto obtain Q measurements using primarily reflection techniques. In thiscase, Δf is found by the difference in frequency between the half powerVSWR frequencies, such that

$\begin{matrix}{{VSWR}_{\frac{1}{2}} = \frac{1 + S_{0} + S_{0}^{2} + {\left( {1 + S_{0}} \right)\sqrt{1 + S_{0}^{2}}}}{S_{0}}} & (17)\end{matrix}$where S_(O) is the VSWR at resonance with a sample in the cavity, andthe 3 db power points correspond to f₁ and f₂ of the two VSWR_(1/2)points.

When the system is undercoupledβ=1/S _(O)  (18)which is substituted to Equation 11, Q_(O)=Q_(L) (1+β), since

$\begin{matrix}{Q_{L} = \frac{f}{\Delta\; f}} & (19)\end{matrix}$where Δf is defined by the VSWR_(1/2) above; Q_(O) due to internallosses only can be found.

As will be recognized to one of ordinary skill in the art, then it isnot necessarily the values of permittivity of the asphalt sample thatare required to be calculated. Rather the density relationship may becompared to any number of parameters measured from the microwavetransmission and reflection loss, frequency shifts, phase shifts, Sparameters, admittance and impedance matrix parameters, etc. That is tosay that the above simply describes one advantageous method to determinethe density of the sample using the reflection and transmissionmeasurements, while the measurements may be related in a number of othermathematically correct methods to the exclusion of having to solve forpermittivity.

The empty cavity in the reflection mode yielded an impedance plot 50 asa function of frequency shown in FIG. 12. Since β<1, the circle ofconstant resistance never crosses the center of the Smith Chart, andβ=1/VSWR=22.2/50=1/2.25. An easy way to find the resonance is to plotthe return loss or S11 in log magnitude and look for the minimum. Thisplot is shown in FIG. 13 and indicates that the frequency of resonanceis 426.7 Mhz. The half power VSWR (Vc) is found to be 7.25, and thiscorresponds to a frequency bandwidth of about 285 Khz for a loaded Q ofQL=1497, and the unloaded Q_(O)=1.444*QL=2162.

Samples were measured using the reflection method. A table of theresults is shown below.

TABLE 4 Frequency Sample Mhz VSWR Ve Bandwidth QL Qo 2-102 368.23 27.7957.63 849 Khz 433 2-202 362.3 64.94 131.9 874.5 414.35 2-301 359.9562.67 127.36 790.5 455.34

Since these VSWR's were so high, the cavity was very much undercoupled,and the unloaded Q will be very close to the loaded Q's.

The resonant frequency can be plotted against the density of the coresfor relative measurements as shown in FIG. 14.PCF=914.24+f*−2.14, r ²=0.99988

Also, the dielectric constant can be calculated using the resonantfrequency and the finite element model of the cavity and these resultswould be identically equal to the results obtained using thetransmission cavity.

It is also notable that for microwave frequencies the calibration isless susceptible to change with the conductance due to moisture of aparticular type of dielectric or pavement. Hence, calibrations may bemore universal from mix to mix. In the microwave region, instead ofmeasuring a lumped impedance, the reflection or transmission propertiesof the device are obtained. As for frequency dependence, the dispersionwill be minimized as f increases as explained below.

For free polar molecules, the orientation and induced polarizations area strong function of temperature; especially at relatively lowfrequencies. For moist (water containing) mixtures,

$ɛ_{r} = {ɛ_{r\;\infty} = \frac{\left( {ɛ_{rs} - ɛ_{r\;\infty}} \right)}{\left( {1 + {j\;\omega\;\tau}} \right)^{\alpha}}}$

where α is a correction for a distribution of relaxation times, τ is therelaxation time directly related to the mobility of the molecules,

_(r∞) is the high frequency permittivity, and

_(rs) is the low frequency or static permittivity. At frequencies wellabove 1/τ,

_(r)=

_(r∞),

_(rs) decreases with rising temperature due to the increasing disorderin the molecules, and τ decreases with increasing temperature. Byinvestigation of the dispersion of the real and imaginary parts of thepermittivity from low frequencies to the microwave band, the moistureeffects may be separated from other attributes such as porosity. For aheterogeneous mixture, these frequency effects will be exacerbated aboveany simple Debye effects as can be explained by the Maxwell-Wagnertheory.

Since asphalt is a “binding” agent and is adsorbed into the aggregates,and since it is a large heavy molecule, the relaxation time is longresulting in relatively low dielectric constants and a low relaxationfrequency. For this reason, microwave analysis of HMA is lesssusceptible to temperature variations when compared to the lower bands.Hence a wideband measurement swept through the microwave band cantherefore result in the separation of moisture and density effects.

U.S. Pat. No. 6,414,497 and U.S. Published patent applications20020175691 discuss the temperature effects of asphalt densitymeasurements. In the microwave region, the temperature effects of polarmolecules are negligible. However there will be temperature effects dueto the simple volume expansion of the material under test. This isbecause the method of measurement is based on the dipole moment per unitvolume of material. In this respect, slight temperature corrections tothe microwave results could be useful for the most accurate results inquality assurance of paving materials. These linear corrections could berelated to the base temperature of the asphalt. For instance, thisexpansion is confirmed by in ASTM standard D 4311-96, “Standard Practicefor Determining Asphalt Volume Correction to a Base Temperature”.

Microwave Planar Circuits

Microwave planar circuits may also be employed especially for use innon-destructive field tests of asphalt. Planar circuits are desirablebecause they include leaky fields configurable as dielectric sensors.FIG. 15 is a plot of slotline impedance vs. asphalt density in themicrowave region, which illustrates that the complex propagationconstant of microwave radiation can be detected using many differentparameters such as complex resonant frequency, complex impedance,complex S parameters etc. The waveguiding or launching device can bemicrostrip, stripline, slotline, coplanar waveguide, circularwaveguides, rectangular waveguides, or even open or leaky waveguidessuch as surface wave launching devices. A planar circuit can measurereflection coefficients or transmission coefficients. These responsesare the direct result of the complex propagation constant in the surfaceof the asphalt and/or traveling across the surface of the asphalt aslaunched from a planar circuit. In microwave propagation, the resonatoris just one means to measure the complex propagation constant α+jβ. Thecircuits mentioned above are a means to measure the complex propagationconstant and S parameters through network analysis. The transmissionline could also be loaded with a device that interacted with thematerial. The resulting impedance shift as a function of density couldbe detected at the input port through phase or resonance using networkanalysis.

Asphalt, in particular, is a complex molecule consisting of heteroatomssuch as sulfur, nitrogen, and oxygen attached to the principle atoms ofcarbon and hydrogen. The resulting configurations are polar because ofan imbalance of electrochemical forces in the bond. The asphaltenes aregenerally dark brown, friable solids and are the most complex componentsof the cement with the highest polarity. The remaining components areresins and oils.

Because the asphalt possesses a permanent dipole moment, and is acomplex chemical, it will have a distribution of relaxation timesleading to the Cole-Davidson equationε_(r)=ε_(r∞)+(ε_(rs)−ε_(r∞))/(1+jωτ)^(α) −jσ/ωε ₀Where the “s” signifies the low frequency permittivity, and the ∞signifies a high frequency permittivity. The last term is included torepresent the losses from the carbon atoms or DC conductance. Thefrequency dependent term in the above equation is in the denominator,which also varies with the relaxation time τ, the inverse of therelaxation frequency. So the mobility of the molecules or ability of themolecules to rotate is defined by the relaxation time, which alsodefines the “boundary” of the materials low and high frequency response.Since asphalt is a solid or semi-solid at room temperature, and is usedas cement, it is understandable that the relaxation frequency will below, and the permittivity will not be large as a result. In the mix, theasphalt is adsorbed onto the aggregate, which further “locks” themolecular movement. Typically the dielectric constants will be less than7. When the asphalt is more liquid, the dipoles will rotate easier,increasing the relative permittivity. This is due the thermal breakingof the bonds. A measure of the strength of molecular binding is theenergy released per mole when the bonds are formed. This is theactivation energy Q. In general the dependence of the relaxationfrequency on the activation energy and temperature is f∝exp(−αQ/T) whereT is degrees Kelvin and α is a proportional constant. As T increases,the relaxation frequency follows.

Because the asphalt is a heterogeneous material which can be moist,there exist free ions and charges that can form on the particularaggregates. This leads to a Maxwell-Wagner effect whereby at the lowerfrequencies, extremely large permittivities are apparent. Since this isalso a polar mechanism, this large “artificial” permittivity is alsoextremely frequency and temperature dependent. However, because of thereduced mobility or large relaxation time τ associated with thisphenomenon, most of these effects are nonexistent in the VHF band andabove. For moist soils, the dispersion can be extreme. A measure of thechange in complex permittivity at microwave frequencies and below canlead to a measure of soil porosity.

Microstrip Surface Gauge

One microwave density device is the microstrip resonator that may bemore practical in non-destructive field tests of asphalt. In this casethe microstrip is an embodiment of the DUT from FIGS. 1 and 2. One suchmicrostrip 60 is shown in FIG. 16(a). The microstrip line 60 is employedas a waveguiding device, and since it is an open structure, the fieldsextend into the space above the line. This is a desirable characteristicfor a sensor. By increasing the thickness h, of the substrate 62, anddecreasing the permittivity of the substrate 62, more of the field willpropagate in the space above the strip as shown in FIG. 16(a). Bycoupling into the strip with an impedance discontinuity, thetransmission line will resonate. For example, placing a material 64(FIG. 16(b)) of higher dielectric constant in the space adjacent theline, even more of the energy will exist in the material 64. This isreferred to as inverted microstrip, and as the dielectric constant ofthe material 64 is increased, the phase velocity will decrease, and theresonator will decrease its resonant frequency.

Much like the method employed above in conjunction with the cavityresonator, the Q and resonant frequency can be measured by the networkanalyzer and the effective permittivity ε′−jε″ can be found. Note thatin FIG. 16(b), the asphalt would act as the upper dielectric layer. Inone useful embodiment the microstrip is a meander line microstrip 66, asillustrated in view of FIG. 16. Ring resonators are very convenientgeometries as well. In these examples, the transmission lines wereoperated as two port structures. However one port devices can also beused such as a resonant “cavity backed dipole.” The resonance may beexclusively the dipole, or a slot antenna excited by microstrip. It mayalso be a cavity backed slot antenna or the result of a tuned shortdipole/transmission line circuit.

The microstrip resonator operates in the same principle as the waveguideresonator with a few significant differences. Like the cavity, the shiftin frequency can be measured and the Q_(L) value is

$\begin{matrix}{Q_{L} = \frac{f}{\Delta\; f}} & (20)\end{matrix}$

Where Δf is usually defined by the −3 dB frequency values off maximum ofS21. Using an effective real permittivity for the measurement volume ofthe resonator (a portion of the field fills the resonator), theimaginary part of the permittivity is

$\begin{matrix}{ɛ_{re}^{''} = \frac{ɛ_{re}^{\prime}}{Q_{Asphalt}}} & (21)\end{matrix}$As resonance occurs approximately when

$\begin{matrix}{{L = {n\frac{\lambda_{g}}{2}}}{and}} & (22) \\{\frac{c}{\sqrt{ɛ_{re}}} = {f\;\lambda_{s}}} & (23)\end{matrix}$Then at the second harmonic, n=2,

$\begin{matrix}{ɛ_{re}^{\prime} = \left( \frac{c}{fL} \right)^{2}} & (24)\end{matrix}$It is also a reasonable assumption that

$\begin{matrix}{\frac{1}{Q_{Asphalt}} = {\frac{1}{Q_{L\; 2}} - \frac{1}{Q_{air}}}} & (25)\end{matrix}$Then the imaginary permittivity of the asphalt is approximated as

$\begin{matrix}{ɛ_{r}^{''} = \frac{ɛ_{re}}{Q_{Asphalt}}} & (26)\end{matrix}$The resonant condition is perturbed from Equation (22) by the couplingstructure. For instance, the coupled transmission line would have aminimum reflection coefficient and/or a maximum transmission coefficientwhen the impedance of the load is transferred to the complex conjugateat the input reference plane. Again, this is a function of the distancebetween the input and output launching structures and the propagationconstant of the traversing wave. The launching structures could be ashort section of microstrip line fed with an SMA connector and loop orgap coupled, or an antenna capable of launching microwave fields with aparticular field orientation such as parallel to the surface of thewaveguide/asphalt interface. Parallel fields are less susceptible tosurface roughness (air gaps between the sensor and the material) thanperpendicular Electric fields.

The following sample measurements included collecting the resonantfrequency of the second harmonic, and the Q value of a microstripresonant structure similar to FIG. 17. These measurements were in therange of 680 Mhz. The second harmonic will have a maximum electric fieldat both the ends of the resonator, as well as the center. These resultswere compared to the known density, which was resolved from a nucleardensity gauge.

FIG. 18 shows the response of the resonant frequency to changes indensity. Here, back calculation of dielectric constant is not required,and it is apparent frequency and density are therefore sufficient tocalibrate the measurements. In FIGS. 19(a)-(b), both the real andimaginary frequencies were incorporated into the analysis yielding aloaded Q factor to changes in density, a two parameter curve fit. Thecurves of FIGS. 19(a)-(b) provided more consistent results. These twofigures also illustrate that both the Q value and the resonant frequencybehave in a linearly decreasing manner as the density increases for themicrostrip device.

Surface Roughness Correction

While it is preferable that the surface of the asphalt sample be smoothor have a known roughness such samples are not practicable in the fieldor in the laboratory. Accordingly, it is desirable to include aroughness correction in conjunction with either or both of theembodiments of a density gauge described above. One embodiment of aroughness gauge is an electromagnetic system having two permittivitysensors. One sensor reads shallow (˜0.25″) depths below the surface, anda second sensor reads deeper (>2″), but also includes the shallow layerin its measurement volume. The sensor is electromagnetic, and uses thepermittivity of the material to calculate the roughness. In oneembodiment, the shallow sensor ran at 50 MHz and was a fringing fieldcapacitance sensor such as disclosed in U.S. Pat. No. 6,803,771,incorporated herein by reference, while the deeper sensor was amicrowave traveling wave type resonator, such as illustrated in FIG. 17.If the mix is constant over the two-inch depth, then it is reasonable toexpect that the surface texture will affect the shallow sensor more thanthe deep sensor.

Since it is extremely difficult to obtain perfect asphalt cores orslabs, a finite element simulation model validates the measurementsdifferences. One embodiment is shown in FIG. 20 wherein the microwavedevice is a covered microstrip line 70 on a substrate 72 of thickness hplace on asphalt 76 having a roughness 74. By solving for thepropagation constant of the strip, the effective permittivity of theentire structure is determined. Resonant frequencies can then be foundusing the actual device dimensions.

This microstrip resonator 70 is 0.304 m long, 9.92 mm wide with gapcoupling. A 1/32″ thick epoxy FR-4 cover is glued directly on the stripas shown in FIG. 20. It was determined using the HP dielectric probethat this cover had

=4.0. The substrate 72 was 0.125″ thick and is Polyflon Norclad,

=2.55. In the simulations, the rough layer 74 was held at 0.25 inchesdeep, but the dielectric constant of this layer was adjusted from equalthe underlying asphalt 76, to 50% less the asphalt value. Note that therough layer has a permittivity that is equal to or less than theasphalt, because of the surface voids represented with the jagged lineat the asphalt interface in FIG. 19.

Five sets of simulations were run at 600 MHz with different asphaltpermittivities. These were

=3.0, 4.4, 6.17, and 7.11. These are all values of materials that areavailable in the lab. For each set of simulations, the asphaltdielectric constant was held constant, while the rough layerpermittivity was changed. For each simulation, the rough layer wasadjusted to correspond to a percent of the asphalt 6, mainly 100%, 90%,80%, 60%, and 50%, except for the asphalt

=6.17, where 68% was used. The 68% was chosen so that the rough layersimulation would have a permittivity corresponding to FR-4 forlaboratory verification.

The effective dielectric constant,

_(re), of the (combined) substrate, cover, roughness layer, and asphaltwas determined. The simulations were calibrated to remove the effects ofthe substrate by simulating the resonator on the known materials andobtaining the resonant frequency and Q value. A calibration curve andequation of the resonant frequency vs. the external material propertiescan be determined. Hence, absolute permittivities of any flat sample cannow be obtained. From the model, the following results were obtained.

TABLE 5 Asphalt 

 = 7.11 Roughness Layer ¼ in. Thick Composite Asphalt = 7.11

 _(re) of structure Permittivity Rough = 7.11 3.43 7.112 Rough = 6.43.35 6.661 Rough = 5.7 3.27 6.209 Rough = 4.27 3.08 5.137 Rough = 3.552.97 4.517 Rough = 7.725 * 

 _(re) − 19.46 Asphalt 

 = 6.17 Composite Asphalt = 6.17

 _(re) Permittivity Rough = 6.17 3.26 6.153 Rough = 5.55 3.19 5.758Rough = 4.94 3.12 5.363 Rough = 4.2 3.03 4.855 Rough = 3.1 2.87 3.952Rough = 7.875 * 

 _(re) − 19.57 Asphalt 

 = 4.4 Composite Asphalt = 4.4

 _(re) Permittivity Rough = 4.41 2.95 4.404 Rough = 3.96 2.90 4.122Rough = 3.52 2.84 3.783 Rough = 2.64 2.72 3.106 Rough = 2.2 2.66 2.768Rough = 7.50 

 _(re) − 17.76 Asphalt 

 = 3.0 Composite Asphalt = 3.0

 _(re) Permittivity Rough = 3.0 2.7  2.993 Rough = 2.7 2.66 2.768 Rough= 2.4 2.62 2.542 Rough = 1.8 2.54 2.091 Rough = 1.5 2.49 1.808 Rough =7.22 

 _(re) − 16.49

Note that the first assignment to the rough layer is the value of theasphalt (2^(nd) row of each table). With both layers assigned the samepermittivity, the simulated calibration of a homogeneous smooth sampleis accomplished by plotting the

_(re) vs. the assigned external material property. Combining with thedata of Table 1, we obtain the composite permittivity,

_(external)=5.642*

_(re)−12.24.  (27)where “external” represents the permittivity of the material excludingthe microstrip substrate and cover. This equation is shown in FIG. 21and represents the data of row 2 in the table for each

_(r)=7.11, 6.17, 4.4, 3.0. Note that FIG. 21 relates only to theperfectly smooth and homogenous surface. In other words, the asphaltlayer and the rough layer have been assigned the same value. As thesurface becomes textured, the permittivity of the rough layer willdecrease. This will decrease the effective permittivity of the entirestructure, even if the asphalt layer does not change. Equation (27) isstill used to find this composite

_(r). For the two-sensor system, the shallow sensor will have a largerreduction in permittivity than the deep sensor. It is this principleupon which the correction is based. The surface roughness correctionshould allow for the shallow layer permittivity to decrease, yet stillobtain a good estimate of the permittivity of the deeper layer.

It is noteworthy that different permittivity combinations of asphalt androughness can lead to the same effective or composite dielectricconstant. If the asphalt

_(r)=7.11 and the surface is

_(r)=4.27 then table 1 shows

_(external)=5.137 as measured by the deep sensor. However, if theasphalt

_(r)=6.14 and it is relatively smooth pavement has a surface value of

_(r)=4.68, then the

_(external) is also 5.137; according to table 1. A lower valued asphaltwith a smoother surface could result in a higher effective permittivitythan the higher valued asphalt with the rougher surface. Therefore, inone method a ratio of the shallow sensor/deep sensor result may used forcorrection. This way, for smooth surfaces, the ratio will be 1 and nocorrection is obtained. However, for a rougher surface, the ratio willbe less than 1, but greater than zero, and a larger correction isobtained. For instance, in the example above, the ratios are4.27/5.137=0.83, and 4.68/5.137=0.91. The second example with a factorof 0.91 is smoother than the 0.83 situation, and the correction will bemuch less.

In the finite element simulations, the results

_(re) were converted to the external or “Top” values using Equation (27)of FIG. 21. To obtain a “first guess” of the deep layer dielectricconstant. One possible correction for the actual permittivity could beε₂=(ε_(X)−ε₁)*e ^((K)*^(h1/w))+ε₁  (28)whereK=(w/h ₁)*In(2/(1+1/x)) x=√(1+12h/w),  (29)w is the strip width ⅜″, h₁=¼″ is the thickness of the rough layer, and

_(x),

₁, and

₂ are the independent permittivities of the external layer, rough layerand deep layer respectively. Notice that the externallayer.epsilon.sub.x is the composite response of both the rough and deeplayer, as “measured” by the deep sensor. In Equation (28), as h₁ becomessmall,

₂=

_(x).

Relationships between the external dielectric constant

_(x) and the deep layer permittivity were also considered. A guess of

₂ is found using Equation (28). Taking a known permittivity value forthe asphalt deep layer, and the deep layer “first guess,” Equation (28),experimental results for the deep (D) and shallow (S) sensors can becompared to the ratio of the first guess (

₂) and known asphalt values (

_(known)). The finite element analysis calculated compositepermittivities were used to obtain the values for the deep and shallowsensors. The experimental results indicate that the ratio of themeasured shallow and deep sensors is related to the ratio of the deeplayer and the composite layer. The experimental relationship is linearas shown in FIG. 22, where in this example the slope is 1.5187 and theintercept is 0.5184.

For example, suppose that the shallow sensor measured 5.55 and the deepsensor obtained the composite external dielectric constant of 5.75.Using slope and intercept from “first guess” of Equation 28, then thevalue of the asphalt layer would be (see the 6.17 asphalt layer in Table1)(5.55/5.75)*1.5187−0.5184=0.9454 Asphalt=5.86/0.9454=6.20.

Alternatively, it may not be necessary to use the “first guess,” andonly consider the measured values of deep and shallow sensors ascompared to the known value. Therefore, the linear relationship betweenthe ratio of the deep sensor

_(x), and known deep permittivity can be plotted versus shallow sensorand deep sensor ratio values, resulting in a slope of 1.828 and anintercept of 0.8316.

Another roughness correction approach is to use actual core measurementsto calculate the ratios of the known bulk permittivity (

_(known)) vs. the deep and shallow sensor ratios. For example, sincethere are two unknowns in the linear equation of FIG. 22, measurementson a smooth side and a rough side of the same core could be used for theroughness solution. One experimental core a very smooth cleaved side,the “X” side, and a normal rough side, the “O” side. In this example,the bulk permittivity (

_(known)) was measured in the microwave cavity and was found to be 5.75.This bulk number was assumed to be the permittivity just under thesurface. Using the (D) deep microwave sensor and the (S) shallow UHFsensor the following dielectric constants were obtained, in Table 5.

TABLE 5 Sensor “X” = Smooth “O” = Rough Deep 5.7 5.15 Shallow 5.6 4.24S/D 5.6/5.7 4.24/5.15 D/( 

 _(known))  5.7/5.75 5.15/5.75

From this sample, two equations can be determined such that this sampleyields lines“X”5.9913=0.9820*m+b“O”0.8956=0.8233*m+b.

Solving these simultaneously leads toD/Z=S/D*0.6027+0.4  (30)

Therefore, by measuring the material with a deep and a shallow sensor,the composite permittivity found with the deep sensor, D, can beseparated into the two layers, S and the unknown Z, as shown in Equation(30).

Another approach is to measure the two ends of an un-cleaved core, whichtypically have different textures, and to use a least squares method tocalculate the average slope and intercept of Equation (30). Instead ofusing one core with one artificial smooth face and a normal face, a morerealistic approach may be to measure many field mixes made into cores.In this method, it is assumed that the core is homogeneous, and that thesame permittivity should be attained on each face of the sample. Firstthe two sides are labeled as “X” and “O” sides. Then each sample isplaced in a resonant closed cavity and the frequency and bandwidthshifts are recorded. A finite element analysis is run on the cavity andcore dimensions, and the real part of the permittivity is found. Withthis method, the bulk permittivity (

_(known)) is the final result. Next, both the deep sensor (D) and theshallow sensor (S) are used to measure the permittivity of the “X” sideand the “O” side of the puck. It is assumed that any differences inthese two sides are due to the different texture or surface propertiesof the puck on each face. Once a good statistical population of cores ismeasured, a table of S/D, D/(

_(known)) is formed for each sample on each side “X” and “O”.

For example, each face is measured with the shallow sensor (S-200 @ 50MHz) and the deep sensor (BS @ 600 MHz). The ratios S/D for both faces(X, O) are then plotted against the ratios D/C for each core in hopesthat a correlation exists between these results, illustrated in FIG. 23.

The regression analysis indicates thatD/(

_(known))=0.405*S/D+0.566  (31)

With an r² of 0.482, the correlation coefficient may be improved withsensors that have less orientational properties and a better defineddepth dependency, as the regression may indicate that the shallow sensorreads deeper than expected.

Accordingly, the two-layers can be simulated using finite elements toobtain equations that describe the calculation of the deep layerdielectric from the shallow and deep measurements. These equations wouldthen be implemented and the coefficients adjusted for a calibration.Likewise, calibration may be empirical by placing the plates on knowndielectric materials. In another modification of the surface roughnesscorrection meter, the cavity measurements can be used to obtain the lossproperties of the asphalt field or laboratory sample. The loss can beconverted to conductivity, and a skin depth or depth of penetration canbe calculated. It is well known that this depth is a function offrequency. Hence, by proper selection of frequency, an automaticallydepth dependent measurement can be obtained. In a slightly differentembodiment, for surface waves, as the frequency increases, the surfacewaves excited by the sensors will penetrate less. This is due to boththe losses due to the conductance, and the boundary solution toMaxwell's Equations for TE or TM type surface waves as known by thosefamiliar in the art.

Many modifications and other embodiments of the inventions set forthherein will come to mind to one skilled in the art to which theseinventions pertain having the benefit of the teachings presented in theforegoing descriptions and the associated drawings. Therefore, it is tobe understood that the inventions are not to be limited to the specificembodiments disclosed and that modifications and other embodiments areintended to be included within the scope of the appended claims.Although specific terms are employed herein, they are used in a genericand descriptive sense only and not for purposes of limitation.

It will be understood that various details of the presently disclosedsubject matter may be changed without departing from the scope of thepresently disclosed subject matter. Furthermore, the foregoingdescription is for the purpose of illustration only, and not for thepurpose of limitation.

What is claimed is:
 1. A portable microwave material gauge fordetermining a quality property of a pavement material comprising: anelectromagnetic field generator configured to generate at least onemicrowave frequency of an electric field mode that penetrates into amaterial, wherein the material includes a heterogeneous materialincluding at least one of a pavement material and a soil material; amemory storing a calibration data set represented by a frequency domainresponse relationship of known physical properties of a material,wherein the frequency domain response is stored in memory of theportable microwave gauge; a sensor operative of the electric field mode,wherein the sensor is excited by the at least one microwave frequencyand determines a permittivity response of the pavement material to theelectric field as a function of a quality property of the material; andan analyzer configured to correlate the sensor permittivity response tothe calibration data set wherein correlating the response includes usingstored relationships between the material quality and the sensorresponse using calibration samples having changes in permittivity as afunction of quality; wherein the quality property of the pavementmaterial is related to at least one of density, modulus, and moisturecontent; wherein the frequency domain response is related to at leastone of measured magnitude and phase of the sensor permittivity responseas determined by the analyzer; and wherein the electromagnetic fieldgenerator is configured to generate: a single frequency at which thesensor permittivity response varies with compaction of the pavementmaterial; or a range of frequencies by sweeping across a bandwidth inwhich the sensor permittivity response varies with density of thepavement material, wherein the sensor comprises at least one of a planarsensor, a leaky cavity sensor, a subsurface sensor, and a monopole. 2.The portable microwave gauge of claim 1 where the changes inpermittivity are determined by a response of the sensor incorporatingimpedance, admittance, loss, phase shift, scattering parameters,reflection, transmission, VSWR, phase velocity, and combinationsthereof.
 3. The portable microwave gauge of claim 1 wherein the sensorresponse is of at least one or more frequency responses to characterizethe quality property of the pavement material.
 4. The portable microwavegauge of claim 1 wherein the electromagnetic field generator isconfigured to generate a field having at least one of a resonant modeand a non-resonant mode.
 5. The portable microwave gauge of claim 1wherein the electromagnetic field generator is configured to generate anelectromagnetic field between 300 MHz and 10 GHz.
 6. The portablemicrowave gauge of claim 1 wherein the electromagnetic field generatoris configured to generate an electromagnetic field of 1 GHz.
 7. Theportable microwave gauge of claim 1 wherein the electromagnetic fieldgenerator is configured to generate an electromagnetic field of 2.5 GHz.8. A portable microwave material gauge of claim 1 wherein the qualityproperty is at least one of asphalt density and soil moisture.
 9. Aportable microwave material gauge of claim 1 wherein the qualityproperty is a modulus property of concrete or asphalt.
 10. A portablemicrowave material gauge of claim 1 wherein the analyzer is configuredto correlate the changes in response to one of a volumetric property anda mechanistic property of the material.
 11. The portable microwavematerial gauge of claim 1 wherein the analyzer corrects for the qualityproperty of the material based on measured material temperature.
 12. Theportable microwave material gauge of claim 11 wherein the temperaturecorrection is related to volumetric expansion of hot asphalt.
 13. Theportable microwave material gauge of claim 11 wherein the analyzer isconfigured to determine a corrected relative density of the material,moisture content of the material, or quality property of a concretematerial.
 14. The portable microwave material gauge of claim 1 whereinthe analyzer is configured to receive a calibration data set of sampleshaving changes in permittivity as a function of known quality propertiesof the material wherein the changes in permittivity determine theresponse of the sensor and the sensor response is measured using atleast one of impedance, admittance, loss, phase shift, scatteringparameters, reflection, transmission, VSWR, phase velocity, andcombinations thereof.
 15. The portable microwave material gauge of claim1, wherein the sensor is operating as at least as one of a one port ormulti port device.
 16. A method for determining a quality property of apavement material comprising a portable microwave gauge including:generating an electromagnetic field producing at least one microwavefrequency of an electric field mode that penetrates into a materialwherein the material includes a heterogeneous mix including at least oneof a pavement material, an aggregate material, and a soil material;incorporating a calibration data set represented by a frequency responserelationship of known physical properties of a material, wherein thefrequency response relationship is stored in memory of the portablemicrowave gauge as at least one of an equation or table; measuring usinga sensor of size and shape to support the electric field mode, beexcited by the at least one microwave frequency, and to determine apermittivity response of the pavement material to the electric field asa function of a quality property of the material; and correlating thesensor permittivity response to the calibration data set or relationwherein correlating the response includes using stored relationshipsbetween the material quality property and the sensor response usingcalibration samples having changes in permittivity as a function ofquality, wherein the response is related to at least one of measuredmagnitude and phase of the sensor permittivity response as determined byan analyzer; wherein the sensor comprises at least one of a planarsensor, a leaky cavity sensor, a subsurface sensor, and a monopole; andwherein the electromagnetic field is generated: at a single frequency atwhich the sensor permittivity response varies with compaction of thepavement material; or across a range of frequencies by sweeping across abandwidth in which the sensor permittivity response varies with densityof the pavement material.
 17. A system comprising: a portableelectromagnetic sensor for determining a quality property of a pavementmaterial wherein a measurement of the sensor and system produces animpedance response based on permittivity of the pavement material; andan analyzer configured to correlate the impedance response of theportable electromagnetic sensor to a density of the pavement materialusing an independent calibration data set or relationship between ameasured permittivity response of the portable electromagnetic sensorand density of the pavement material, wherein the measured permittivityresponse of the portable electromagnetic sensor is related to at leastone of a measured magnitude and phase of the sensor permittivityresponse as determined by the analyzer; wherein the portableelectromagnetic sensor comprises at least one of a planar sensor, aleaky cavity sensor, a subsurface sensor, and a monopole; and anelectromagnetic field generator configured to generate: a singlefrequency at which the permittivity of the pavement material varies withcompaction of the pavement material; or a range of frequencies bysweeping across a bandwidth in which the permittivity of the pavementmaterial varies with density of the pavement material.
 18. The portablemicrowave material gauge of claim 1, wherein the measured magnitude andphase of the sensor permittivity response are related to scatteringparameters as attained by a network.
 19. The portable microwave materialgauge of claim 18, wherein the scattering parameters comprise impedance,admittance, VSWR and reflection or transmission coefficients.
 20. Theportable microwave material gauge of claim 1, wherein determining thepermittivity response includes determining a change in the permittivityas a function of a change in the quality property of the material. 21.The method of claim 16, wherein determining the permittivity responseincludes determining a change in the permittivity as a function of achange in the quality property of the material.